Ioannis G. Ntagkas

This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progress

Empirical philosophers of science aim to base their philosophical theories on observations of scientific practice. But since there is far too much science to observe it all, how can we form and test hypotheses about science that are sufficiently rigorous and broad in scope, while avoiding the pitfalls of bias and subjectivity in our methods? Part of the answer, we claim, lies in the computational tools of the digital humanities, which allow us to analyze large volumes of scientific literature. Here we advocate for the use of these methods by addressing a number of large-scale, justificatory concerns—specifically, about the epistemic value of journal articles as evidence for what happens elsewhere in science, and about the ability of DH tools to extract this evidence. Far from ignoring the gap between scientific literature and the rest of scientific practice, effective use of DH tools requires critical reflection about these relationships.

ABSTRACT The target article uses the metaphysics of properties to make its meta-ethical claims. This comment discusses two general points in the metaphysics of properties. The first point has to do with the conditions for property identity. Philosophers who accept the existence of properties have proposed a variety of criteria for their identity. The standard Broome applies is medium coarse. Other standards for property identity could be evaluated for their appropriateness for addressing questions in the metaphysics of ethics. Use of a formalized theory of properties might help in such an evaluation. The second point has to do with Broome’s suggestion of a distinction between a property and a reified property. A suggestion will be offered for a range of ways such a distinction could be filled out using the resources of a formalized theory of properties and objects. Objects will be proposed that could serve as Broome’s reified properties.

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ‘diagonal argument’ and, moreover, one used to establish a positive conclusion rather than a paradox.

I propose a straightforward reconciliation of Leibniz’s conception of bodies as aggregates of simple substances (i.e., monads) with his doctrine that bodies are the phenomena of perceivers, without in the process saddling him with any equivocations. The reconciliation relies on the familiar idea that in Leibniz’s idiolect, an aggregate of Fs is that which immediately presupposes those Fs, or in other words, has those Fs as immediate requisites. But I take this idea in a new direction. Taking notice of the fact that Leibniz speaks of three respects in which one thing may immediately presuppose others--i.e., with respect to its being, its existence, and its reality--I argue that a phenomenon having its being in one perceiving substance (monad) can plausibly be understood to presuppose other perceiving substances (monads) in two of these respects. Accordingly, good sense can be made of both the claim that a phenomenon in one monad is an aggregate of other monads (in Leibniz’s technical sense of 'aggregate') and the (equivalent) claim that the latter monads are constituents of the phenomenon (in his technical sense of 'constituent'). So understood, the two conceptions of body are perfectly compatible, just as Leibniz seems to think.

In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this paper, we describe what we have discovered when the theory of abstract objects is implemented in PROVER9 (a first-order automated reasoning system which is the successor to OTTER). After reviewing the second-order, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in PROVER9's first-order syntax, and (2) how PROVER9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research.

In the tradition of Denotational Semantics one usually lets program constructs take their denotations in reflexive domains, i.e. in domains where self-application is possible. For the bulk of programming constructs, however, working with reflexive domains is an unnecessary complication. In this paper we shall use the domains of ordinary classical type logic to provide the semantics of a simple programming language containing choice and recursion. We prove that the rule of {\em Scott Induction\/} holds in this new setting, prove soundness of a Hoare calculus relative to our semantics, give a direct calculus ${\cal C}$ on programs, and prove that the denotation of any program $P$ in our semantics is equal to the union of the denotations of all those programs $L$ such that $P$ follows from $L$ in our calculus and $L$ does not contain recursion or choice.

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. Those assumptions arguably include some necessitist principles. Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic.

We develop a theory of necessity operators within a version of higher-order logic that is neutral about how fine-grained reality is. The theory is axiomatized in terms of the primitive of *being a necessity*, and we show how the central notions in the philosophy of modality can be recovered from it. Various questions are formulated and settled within the framework, including questions about the ordering of necessities under strength, the existence of broadest necessities satisfying various logical conditions, and questions about their logical behaviour. We also wield the framework to probe the conditions under which a logicist account of necessities is possible, in which the theory is completely reducible to logic.

Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think that there is some sense in which arithmetic is true and determinate.

In recent years what has come to be called the 'New Mechanism' has emerged as a framework for thinking about the philosophical assumptions underlying many areas of science, especially in sciences such as biology, neuroscience, and psychology. This book offers a fresh look at the role of mechanisms, by situating novel analyses of central philosophical issues related to mechanisms within a rich historical perspective of the concept of mechanism as well as detailed case studies of biological mechanisms. It develops a new position, Methodological Mechanism, according to which mechanisms are to be viewed as causal pathways that are theoretically described and are underpinned by networks of difference-making relations. In contrast to metaphysically inflated accounts, this study characterises mechanism as a concept-in-use in science that is deflationary and metaphysically neutral, but still methodologically useful and central to scientific practice.

According to a simple Bayesian argument from evil, the evil we observe is less likely given theism than given atheism, and therefore lowers the probability of theism. I consider the most common skeptical theist response to this argument, according to which our cognitive limitations make the probability of evil given theism inscrutable. I argue that if skeptical theists are right about this, then the probability of theism given evil is itself largely inscrutable, and that if this is so, we ought to be agnostic about whether God exists.

The existence and fundamentality of spacetime has been questioned in quantum gravity where spacetime is frequently described as emerging from a more fundamental non-spatiotemporal ontology. This is supposed to lead to various philosophical issues such as the problem of empirical coherence. Yet those issues assume beforehand that we actually understand and agree on the nature of spacetime. Reviewing popular conceptions of spacetime, we find that there is substantial disagreement on this matter, and little hope of resolving it. However, we argue that this should not trouble us as these issues, which seem to suggest the need for an account of spacetime in quantum gravity, can be addressed without one.

This book provides an up-to-date overview of the foundations of spacetime physics. It features original essays written by world-class experts in the physics and philosophy of spacetime. The foundational questions regarding the origin and nature of spacetime are branching into new and exciting directions. These questions are not restricted to the quantum gravity program but also arise in the context of a well-established theory like general relativity. Against the background of these quick and diverse developments, this volume features a broad range of perspectives on spacetime. Part I focuses on the nature of spacetime in non-quantum theories, such as Newtonian mechanics and relativity. Part II explores some intriguing conceptual implications of developing a quantum theory of spacetime. The Foundations of Spacetime Physics is an essential resource for scholars and advanced students working in philosophy of physics, philosophy of science, and scientific metaphysics.

Belief polarization occurs when subjects who disagree about some matter of fact are exposed to a mixed body of evidence that bears on that dispute. While we might expect mutual exposure to common evidence to mitigate disagreement, since the evidence available to subjects comes to consist increasingly of items they have in common, this is not what happens. The subjects’ initial disagreement becomes more pronounced because each person increases confidence in her antecedent belief. Kelly aims to identify the mechanisms that underlie this phenomenon and assess whether these processes undermine the justification of polarized beliefs. He concludes that given evidentialism, justification is not undermined by the polarizing mechanisms. I take on board Kelly’s description of the polarizing mechanisms, but challenge his conclusion. I argue that on plausible versions of evidentialism, the beliefs that result from these routes to polarization are not justified.

Epistemic contextualism is a recent and hotly debated topic in philosophy. Contextualists argue that the language we use to attribute knowledge can only be properly understood relative to a specified context. How much can our knowledge depend on context? Is there a limit, and if so, where does it lie? What is the relationship between epistemic contextualism and fundamental topics in philosophy such as objectivity, truth, and relativism? The Routledge Handbook of Epistemic Contextualism is an outstanding reference source to the key topics, problems, and debates in this exciting subject and is the first collection of its kind. Comprising thirty-seven chapters by a team of international contributors the _Handbook_ is divided into eight parts: Data and motivations for contextualism Methodological issues Epistemological implications Doing without contextualism Relativism and disagreement Semantic implementations Contextualism outside ‘knows’ Foundational linguistic issues. Within these sections central issues, debates and problems are examined, including contextualism and thought experiments and paradoxes such as the Gettier problem and the lottery paradox; semantics and pragmatics; the relationship between contextualism, relativism, and disagreement; and contextualism about related topics like ethical judgments and modality. The Routledge Handbook of Epistemic Contextualism is essential reading for students and researchers in epistemology and philosophy of language. It will also be very useful for those in related fields such as linguistics and philosophy of mind.

Abstract: According to the Veridicality Thesis, information requires truth. On this view, smoke carries information about there being a fire only if there is a fire, the proposition that the earth has two moons carries information about the earth having two moons only if the earth has two moons, and so on. We reject this Veridicality Thesis. We argue that the main notions of information used in cognitive science and computer science allow A to have information about the obtaining of p even when p is false.

Modality - the question of what is possible and what is necessary - is a fundamental area of philosophy and philosophical research. The Routledge Handbook of Modality is an outstanding reference source to the key topics, problems and debates in this exciting subject and is the first collection of its kind. Comprising thirty-five chapters by a team of international contributors the Handbook is divided into seven clear parts: worlds and modality essentialism, ontological dependence, and modality modal anti-realism epistemology of modality modality in science modality in logic and mathematics modality in the history of philosophy. Within these sections the central issues, debates and problems are examined, including possible worlds, essentialism, counterfactuals, ontological dependence, modal fictionalism, deflationism, the integration challenge, conceivability, a priori knowledge, laws of nature, natural kinds, and logical necessity. The Routledge Handbook of Modality is essential reading for students and researchers in epistemology, metaphysics and philosophy of language. It will also be very useful for those in related fields in philosophy such as philosophy of mathematics, logic and philosophy of science.

This collection highlights the new trend away from rationalism and toward empiricism in the epistemology of modality. Accordingly, the book represents a wide range of positions on the empirical sources of modal knowledge. Readers will find an introduction that surveys the field and provides a brief overview of the work, which progresses from empirically-sensitive rationalist accounts to fully empiricist accounts of modal knowledge. Early chapters focus on challenges to rationalist theories, essence-based approaches to modal knowledge, and the prospects for naturalizing modal epistemology. The middle chapters present positive accounts that reject rationalism, but which stop short of advocating exclusive appeal to empirical sources of modal knowledge. The final chapters mark a transition toward exclusive reliance on empirical sources of modal knowledge. They explore ways of making similarity-based, analogical, inductive, and abductive arguments for modal claims based on empirical information. Modal epistemology is coming into its own as a field, and this book has the potential to anchor a new research agenda.

In the main article on Leibniz, it was claimed that Leibniz's philosophy can be seen as a reaction to the Cartesian theory of corporeal substance and the necessitarianism of Spinoza and Hobbes. This entry will address this second aspect of his philosophy. In the course of his writings, Leibniz developed an approach to questions of modality—necessity, possibility, contingency—that not only served an important function within his general metaphysics, epistemology, and philosophical theology but also has continuing interest today. Indeed, it has..

The seventeenth century saw a major revolution in our ways of thinking about such issues as the method appropriate to philosophy and science, the relation between mind and body, the nature of substance, and the place of humanity in nature. While not neglecting the lesser but still influential figures, such as Arnauld and Malebranche, John Cottingham focuses primarily on the three great "rationalists": Descartes, Spinoza, and Leibniz. He examines how they approached central problems of philosophy, and shows how closely their ideas are related, despite the radically different philosophical systems they produced. He not only places the major thinkers in their historical and philosophical contexts, but engages their ideas in a vigorously critical way, revealing their capacity to throw light on major philosophical topics that are still very much alive today.